Effective dynamics for ferromagnetic thin films: a rigorous Justification

Landau-Lifshitz-Gilbert dynamics governs the evolution of magnetization in a ferromagnetic body. It is a damped Hamiltonian system, describing the combined effect of gyromagnetic precession and damping.

Our attention is on ferromagnetically soft thin-film elements. They are used in many divices and have been explored at length experimentally and numarically. Since for thin films the aspect ratio is small, it it natural to seek a two-dimentional effective equation, expressing the asymptotic dynamics in the limit as the aspect ratio tends to zero. Such an equation is obtained in a regime.